Eevee bump and displacement modifiers are low resolution?
It is caused by the library that EEVEE use:

Documentation


  Material
  
  Bump Mapping
  
  As of now, bump mapping is supported using OpenGL derivatives which are the same for each block of 2x2 pixels. This means the bump output value will appear pixelated. It is recommended to use normal mapping instead.
  
  
    Tips: If you absolutely need to render using Bump nodes, render at twice the target resolution and downscale the final output.
  


I try some approach to resolve this problem since about 10 month ago. But there isn't a plausible solution that can be easily done without changing bump map. And 2x resolution suit my application.